Fade a mesh out due to animated distance from Empty
The point is to be relative to the "empty" parent.

For that, use it as input in the texture coordinate node (left).

Then few calculations (simply the distance sqrt(xx+yy+z*z), modulated by the "2" input value), to drive the mix shader. If only the Z interests you, you can simplify that.



if the cube moves :



If the empty moves :